Non-reciprocal wave transmission



Sept. Z7, 1960 R. M. PORTER, JR

NoN-REc1PRocAL WAVE TRANSMISSION 2 Sheets-Sheet 1 Filed March 9, 1954 NSi /Nl/EA/ TOR R. M. PORTER JR.

(iIk Elli J. ab?

ATTORNEY Sept. 27, 1960 R. M. PORTER, JR

NoN-RECIPROCAL WAVE TRANSMISSION 2 Sheets-Sheet 2 Filed March 9. 19542,954,535 Patented Sept. 2'?, i960 2,954,535 NoN-nacrrnccm, WAVETRANSMISSION Roy M. Porter, Jr., Rainbow Lakes, NJ., assignor to BellTelephone Laboratories, Incorporated, New York, NX., a corporation ofNew York Filed Mar. 9, 1954, Ser. No. 414,9;34 '1 Claim. (Cl. 33'3-73)This invention relates to electromagnetic wave transmission systems and,more particularly, to multibranch circuits having frequency selective,non-reciprocal transmission properties for use in said systems.

Recently, the electromagnetic wave transmission art has beensubstantially advanced by the development of a whole new group ofnon-reciprocal transmission components. A large number of these haveutilized one of the non-reciprocal properties of gyromagnetic materials,most often designated ferromagnetic materials or ferrites. One of themore important of these components is known as an isolator in that ithas the property of transmitting wave energy freely in one directionbetween its terminals while resisting transmission in the oppositedirection. It is thus advantageously used between any energy source andits load to prevent reflections from the load from returning to thesource. Another of these components is a multibranch network kno-wn as acirculator circuit that has the electrical property that energy istransmitted in circular fashion around the branches of the network sothat energy appearing in one branch thereof is coupled to only one otherbranch for a given direction of transmission, but to another branch forthe opposite direction of transmission. This circuit property has founduse in numerous applications.

It is an `object of the present invention to establish frequencyselective, non-reciprocal connections between a plurality of branches ofa multibranch network.

It is a further object to provide new types of isolator and circulatorcircuits.

It is a more specific object to establish a` connection between thebranches of a multibranch circuit for one direction of transmission atoine frequency or band of frequencies and for the opposite direction `atanother frequency or band of frequencies.

It has been previously demonstrated that an element of gyromagneticmaterial polarized by a magnetic field will exhibit a differentpermeability to oppositely rotating circularly polarized wavespropagated parallel to the direction of the applied field. In accordancewith the prsent invention, rst and `second wave transmission structuresare coupled through a resonant cavity tuned by such a gyromagneticelement. The transmission structures are coupled to the cavity in aspecial way so that wave energy propagated in a given direction ineither structure will induce circularly polarized waves rotating inrespectively oppo'site senses in the cavity. The strength of thepolarizing iield is adjusted so that the cavity is resonant at selecteddifferent frequencies for these OPPOSitely rotating waves. Thus thecoupling between the rst structure and the second structure throughthetcavity is both` selective as to the direction in which wave energyis propagating in each structure and also to its frequency.

In the trst illustrative embodiment of the invention to be described indetail hereinafter, the cavity is reso'nant at a first frequency :onlyfor wave energy propagating toward it from the first structure and isresonant at a second frequency only for wave. energy `propagating to-rward it from the second structure. Thus only wave energy at the firstfrequency is coupled from the first structure into the second, whereasonly wave energy at the seco'nd frequency is coupled from the secondinto the first. This results in a frequency selective isolator circuit.Energy traveling in the wrong direction and at the wrong frequency forcoupling is reflected into particularly positioned dissipative means.

In a second illustrative embodiment of the invention, energy dissipatedin the first embodiment is coupled into a pair of polarization selectiveconnections, located one on either side of the cavity. 'This results ina four branch, frequency selective circulator in which a non-reciprocalconnection is established in a given sequence between the four branchesat a first frequency and in a reverse sequence at a second frequency.

In another illustrative embodiment of the invention a pair ofrectangular wave guides are coupled to the cavity by means which inducecircularly polarized waves in the cavity that rotate in sensesdetermined by the direction of propagation of the energy in the guides.Thus, four branch, frequency selective circulator action is obtained ina structure of exceedingly simple construction.

These and other objects and advantages, the nature of the presentinvention, and its various features, will appear more fully uponconsideration of the various illustrative embodiments now to bedescribed in detail in connection with the accompanying drawings, inwhich:

Fig. 1 is a perspective view of the present invention showing the firstand second wave guide structures interconnected by a chamber containinga ferromagnetic element;

Fig. 2, given by way of illustration, is the characteristic of the realpermeability of a ferromagnetic element versus the applied magneticiield foi oppositely rotating circularly polarized waves;

lFig. 3 is a perspective view of the second embodiment of the inventionshowing two pairs of orthogonal polarization selective connectionsinterconnected through the ferromagnetically tuned cavity;

Fig. 4 is a schematic representation olf the circulator couplingcharacteristic for the embodiment of Fig. 3;

Fig. 5 is a perspective view of the third embodiment of the inventionshowing a pair of rectangular wave guides interconnected through aferromagnetically tuned cavity; and

Fig. 6 is a schematic representation of the circulator characteristicfor the embodiment of Fig.. 5.

Referring more specifically to Fig. l, a. nonreciprocal two branchisolator circuit is shown as an illustrative embodiment of the presentinvention. This circuit comprises a rst section 11 of conductivelybounded electrical transmission line for guiding wave energy, which maybe a rectangular wave guide having a wide internal crosssectionaldimension of at least one-half wavelength of the energy to be conductedthereby and a narrow dimension substantially one half of the widedimension.` Guide 11 tapers smoothly and gradually into a second section12 of wave guide of a type capable of supporting circularly polarizedwaves, i.e., plane waves for which the electric polarization rotates inspace as the wave propagates. As illustrated, section 12 may be a waveguide of circular cross sectionV having a diameter slightly less thanthe wide dimension of `guide 11, but it may be a guide of square crosssection. The other end of guide 12 tapers into a third section 13 ofrectangular wave guide identical to section 11.

In either end of guide 12 adjacent to guides 11 and 13, respectively,are means for dissipating wave energy polarized in planes perpendicularto the polarization supported by guides 11 and 13. As illustrated, thesemeans comprise a pair of vanes 14 and 15 of resistive material severalwavelengths long, diametrically disposed in guide 12 in the plane of thewave energy to be dissipated. In accordance with the usual practice, theends of vanes 14 and 15 may be tapered to prevent `undue reflection fromthe edges lthereof.

Suitable means for producing a conversion between the linearly polarizedwaves supported by guide 11 and the circularly polarized waves supportedin guide 12'is located in the end of guide 12 adjacent vane 14. Asillustrated, this means may be a 90' degree differential phase shiftsection of any of the types disclosed, for example, in Principles andApplications of Wave Guide Transmission, by G. C. Southworth, 1950,pages 327 throughv 331. By way of specific illustration, the phase shiftsection shown in Fig. 1 comprises two oppositely positioned metal fins16 and 17, each extending perhaps one fourth of the way across guide 12and lying in a plane which -is inclined at 45 degrees counterclockwisefrom the polarization of wave energy in guide 11, as viewed from guide11. As is well known, if the lengths of fins 16 and 17 are such that a90 degree phase shift is introduced to wave energy polarized parallel tothe plane of the fins relative to the wave energy polarizedperpendicular to the plane of the fins, the linearly polarized wave fromguide 11 is converted to and from a counterclockwise rotating circularlypolarized wave in guide 12. A similar pair of fins 18 and 19 is locatedin the end of guide 12 adjacent vane 15. Fins 18 and 19 lie in a planewhich is inclined 45 degrees clockwise from the polarization in guide11, placing them at right angles to theplane of fins 16 and 17.

The heart of the present invention consists of a gyromagnetically tunedresonator comprising a conductive cavitythat is resonant at onefrequency to circularly polarized Waves rotating in one sense andresonant at another frequency to waves rotating in the other sense. Thusa cavity 20 is formed in the central portion of guide 12 betweenreactive iris 21 and reactive iris 22. Iris 21 is spaced from iris 22 ata multiple of one half of the guide wavelength of the rotating waves incavity 20 under the conditions to be defined in detail hereinafter.

Cavity 20 is tuned by a slender cylindrical element 23 of gyromagneticmaterial which is supported axially in cavity 20 by a support 24.Support 24 may be made in any Adesirable shape of a material of lowdielectric constant such as polyfoam. The term gyromagnetic material isemployed here in its accepted sense as designating the class ofmaterials having portions of the atom thereof that are capable of beingaligned by an external magnetic field and capable of exhibiting asignificant precessional motion at a frequency within the microwaverange contemplated by the invention, this precessional motion having anangular momentum, a gyroscopic moment and a magnetic moment. As aspecific example of a gyromagnetic material, element 23 may be made ofany of the several ferromagnetic materials combined in a spinelstructure. For example, element 23 may comprise an iron oxide with asmall quantity of one or more bivalent metals such as nickel, magnesium,zinc, manganese or other similar material, in which the other materialscombined with the iron oxide in a spinel structure. This material isknown as a ferromagnetic spinel or a ferrite. Frequently, thesematerials are first powdered and then molded with a small percentage ofplastic material, such as Teflon or polystyrene. As a specific example,element 23 may be made of nickel-zinc ferrite prepared in the mannerdescribed in the publication of C. L. Hogan, The Microwave Gyrator, inthe Bell System Technical Journal, January 1952, and in his copendingapplication Serial No. 252,432, filed October 22, 1951, now UnitedStates Patent 2,748,353, issued May 29, 1956.

Element 23 is biased by a steady polarizing magnetic field of a strength-to be described. As illustrated in Fig. l, this field is appliedparallel to the `direction of propagation vof the waves in lguide 12 andmay be 4 supplied by a solenoid 25 mounted upon the outside of guide 12and supplied by a source 26 of energizing current. To facilitate theexplanation that follows, specific polarities are assigned to this fieldas indicated on the drawing with the north pole thereof on the endtoward guide 13. Therefore, all reference to clockwise andcounterclockwise hereinafter is taken as viewed in the positivedirection of this field, i.e., as viewed from guide 11 looking towardguide 13. It should be noted, however, that element 23 may be magnetizedin the opposite polarity and by a solenoid of other suitable physicaldesign, by a permanent magnetic structure, or the ferromagnetic materialof element 23 may he permanently magnetized if desired.

The effect of element 23 upon circularly polarized waves in cavity 20may now be considered. This consideration may most readily be made inconnection with the explanatory diagram of Fig. 2 which shows the nowfamiliar characteristic of the Variation of the real permeability of aferromagnetic `element as the applied magnetic field is changed. It willbe seen from curve 30 of Fig. 2 that the permeability for a circularlypolarized wave rotating counterclockwise as viewed in the positivedirection of the applied magnetic field increases from unity as themagnetic field is increased to the saturation point 31, and'then levelsoff to a substantially constant value. vA clockwise rotating wave asrepresented by curve 33 decreases from unity, through zero and furtherdecreases to a negative value. At the magnetic field strength 32producing ferromagnetic resonance in the material, the permeabilitysuddenly changes to a positive value. Cavity 20 of Fig. 1 is thereforeresonant at different frequencies for the oppositely rotating waves dueto this difference in permeability experienced by these waves. Cavity 20may therefore be made resonant at the frequency f1 for circularlypolarized waves rotating in the above defined counterclockwisedirection. Simultaneouslyit may be resonant at the frequency f2 forclockwise rotating waves. The frequency `difference between fl and f2may be controlled over relatively wide limits by the physical size ofelement 23 and by the strength of the applied magnetic field, which inthe usual case is adjusted below the Value producing ferromagneticresonance. The location of frequencies f1 and f2 in the over-allfrequency spectrum is determined by the spacing between iris 21 and iris22. Thus this spacing is equal to a multiple of one half the guidewavelengths of both the clockwise and counterclockwise rotating waves incavity 270. The band-pass characteristic of cavity 20 is determined bythe size and shape of irises 21 and 22 in accordance with conventionalresonator practice. It

is therefore understood that reference hereinafter to f1` and f2includes also the band of frequencies included within the band-passcharacteristic of cavity 20 which have the center frequencies f1 or f2.

It is now possible to describe the over-all mode of operation of theisolator circuit of Fig. 1 by following the path of microwave energyapplied respectively to each of its output terminals. Thus, linearlypolarized wave energy is applied to guide 11, which is assumed toinclude both the frequency components f1 and f2. This wave energytravels past vane 14 inasmuch as it is normal to the plane of the vaneand is converted into a counterclockwise rotating wave by differentialphase shifters 16 and 17. The components f1 of this energy pass throughiris 21, will be resonant in cavity 20 and will be coupled through iris22 into the right-hand portion of guide 12 asa counterclockwise rotatingcircularly polarized wave. This wave is reconverted into a linearpolarization by phase Shifters 18 and 19 in the proper` nent ofthe waveis further shifted by phase Shifters 16 and 17, giving to this componenta total 180 degree differential phase shift so that the total wavepolarization is rotated into the plane of resistive vane'14 by which itis absorbed. Thus only wave energy of the frequencies f1 may passthrough the isolator of Fig. l in a direction from left to right asshown, while the frequencies f2 attempting to pass in this direction aredissipated.

On the other hand, if a similar wave including the frequencies f1 and f2are applied to guide 13 it will be converted by phase Shifters 18 and 19into aclockwise rotating Wave in guide 12. Cavity 2) is resonant at thefrequency f2 and these components are transmitted through the cavity toappear in guide 11 while the cornponents f1 are reilected from thecavity to be dissipated in vane 15.

In Fig. 3 a second embodiment of the invention is shown in which theenergy dissipated in resistive vanes 14 and 15, respectively, of Fig. lis coupled into polarization selective connections 35 and 36,respectively. In other respects the embodiment of Fig. 3 is similar tothat of Fig. l and corresponding reference numerals have been employedto designate corresponding components. As illustrated, polarizationselective connections 35 and 36 each comprise a rectangular wave guidejoined to guide 12 in a shunt or H-plane junction. Thus guides 35 and 36are physically oriented with respect to guides 11 and 13, respectively,so that wave energy in guides 35 and 36 is coupled into circular guide12 as waves polarized perpendicular to the energy introduced by guides11 and 13, respectively. Thus guides 11 and 35 comprise a pair ofpolarization selective connecting terminals by which wave energy in' twoorthogonal polarizations may be coupled to and from one end of guidelZ,While guides 36 and 13 comprise a second pair of such terminals.

In view of the detailed analysis of the embodiment of Fig. 1 givenabove, the operation of the circulator circuit of Fig. 3 may beconveniently explained with reference to the diagram of Fig. 4. `Thus ifwave energy is applied at terminal a to guide 1 1, the components f1thereof will be coupled to terminal b of guide 13, while the componentsf2 thereof will be reected from cavity 21B into guide 35 to appear atterminal d. These frequency selective connections are indicated on Fig.4 by the radial arrows labeled a, b ,andV d, respectively, associatedwith a ring 37 and the arrows 38` and 39. The arrow 38 indicates aprogression at the frequency f1 in the sense from a to b, while thearrow 39 indi- Cates progression at the frequency f2 in the sensefrom dto a. Should a similar Wave be appliediat terminal b to guide 13 it willsimilarly divide on the basis of frequency between terminals a and c asschematically indicated on Fig. 4. The same is true for a Wave appliedat terminal c or at terminal d. 'Ihus a circulator characteristic isobtained for the components f1 in the sequence a-b-c--d-a, while asimilar circulator characteristic is obtained for the components f2 inthe sequence a-dc-b-a.

In Fig. 5, another embodiment of the invention i-s shown comprising apair of spaced, substantially parallel, rectangular Wave guides 40` and41. Guides 40 and 41 are coupled by a guide 42 which m-ay have either acircular or a square cross section. Guide 42 abuts the wide walls 44 and45 of guides 40 and 41, respectively. An aperture L18- 49, the nature ofwhich will be considered hereinafter, couples wave energy in guide 40 toand from guide 42, While an aperture 50-51 couples wave energy in guide41 to and from guide 42. Thus a cavity 43 is formed between wall 44 ofguide 40 and wall 45 of guide 41. Cavity 43 is tuned by a gyromagneticelement 46 and therefore has the properties for counterclockwse andclockwise rotating circularly polarized waves, respectively, as definedabove for cavity 20 of Fig. 1.

The manner in which these waves are excited in cavity 43 may now beexamined. For this purpose it will be convenient to locate guides 40 and41 :in a coordinate system as represented by the divergent vectors 47,labeled x and z. The vector x indicates a positive sense along thetransverse Wide dimensions of guides. 40 and 41 and z indicates apositive sense along their longitudinal direction of propagation.Therefore the predominantly transverse magnetic field components of adominant mode Wavein guide 41 at a particular instant of time are shownin` Fig. 5 and labeled HX, while the predominantly longitudinalcomponents are labeled HZ. These components form loops which lie inplanes parallel to the wide dimensio-n of guide 41. The arrows on theindividual loops 52 and 53 indicate their polarity at a given instant oftime and their sense is arbitrarily defined by the coordinates 47.

Aperture 50-51 is located in the top Wall of guide 41 at a point off thecenter line thereof which places the aperture at a point having both HXand Hz components. Slot 51 of aperture 50-51 is parallel to andtherefore effective for coupling the HZ components into cavity 43 ofguide 42, while slot 50 thereof is parallel to and therefore effectivefor coupling the Hx components. The amplitudes of these two componentsin guide 42 should be equal and this is obtained if slots 50 and 51 areof identical sizes and their intersection is located at the point in thetop wall of -guide 41 at which the HZ and Hx components are of equalamplitude. The point may be moved toward the center of the wall(stopping short of precise center) if the size of slot 51 iscorrespondingly increased and slot 50 decreased. tI-f the aperture islocated at the exact point of equal Hz and HX components in guide 41,the aperture may be simply one of circular or square shape. The abuttingend of guide 42 may be centered above aperture 50-51. The shape ofaperture 48-49 in wall 44 may be identical to aperture Stb-51 ifdesiredand if it comprises a crossed slot as shown, the slots may be alignedrespectively with slots 50 and 51.

The relative phases of the components coupled from guide 41 into cavity43 depend upon the direction of propagation of the wave energy in guide41. When the Wave in guide 41 is propagating in the positive directionthe component HZ of loop 5'2 is increasing to its maximum negative valuewhile the component HX is decreasing from its maximum positive value. Inother Words, the component HZ is in a phase degrees ahead in time fromthe component HX and this produces in cavity 43 a counterclockwiserotating circularly polarized Wave. Now, when the wave in guide 41 ispropagating in the negative direction the component Hz of loop 52 isincreasing to its maximum positive value while the component HX isdecreasing from its maximum positive value. Hz is ytherefore 90 degreesbehind in time from the component HX and this produces in cavity 43 aclockwise rotating circularly polarized wave.

It is realized, of course, that the specific reference to positive andnegative values and to ahead and behind in time are completely arbitraryand apply only to the illustrative senses shown on Fig. 1. Also, a phasedelay of 90 degrees which is inherent in any coupling through anaperture has been disregarded inasmuch as it affects all componentsalike. This explanation does, however, serve to demonstrate that for onedirection of propagation past the aperture 50--51, the wave induced incavity 43 will rotate in one sense, while for the opposite direction ofpropagation the induced wave will rotate in the opposite sense. Sinceguide 40 bears the same relationship to guide 42 as does guide 41, italso demonstrates that waves propagating tin the same direction in both`guides 40 and 41 will induce similarly rotating components 4in guide42. In this respect the structure of Fig. 5 is symmetrical.

It is now possible to describe the over-all operation of the embodimentof Fig. 5 by following the path of Wave energy applied at its severalterminals. Therefore, assume that Wave energy, including the frequencycomponents f1 for which cavity 43 is resonant for counterclockwiserotating components, the frequency components f2 for which cavity 43 isresonant for clockwise rotatingv components, and the frequencycomponents fn which comprise other components outside the band of eitherf1 or f2, is applied to the left-hand end of guide 41 by way of terminala. This energy tends to produce a countercloclcwise rot-ating wave incavity 18. The f2 and fn components thereof are not resonant in cavity18 and will pass on the right-hand end of .guide 41 to appear interminal d. This connection is indicated schematically on Fig. 6 by thearrows labeled a and d associated with ring 55 and the arrows 56 and 57which indicate progression at the frequencies f2 and fn, respectively,in the sense from a to d.

The f1 components of the applied wave energy produce a counterclockw-iserotating wave which is resonant in cavity 43, will be coupled throughaperture 48-49 into guide 40 as a positive z-direction componentfollowed 90 degrees later in time by a positive x-direction component.As noted above, it is the wave transmitted in the positive z-directionin guide 40 that has this phase relationship. Conversely, `this phaserelationship between the exciting components will produce a Wavepropagated only in the positive direction in guide 40 toward terminal b.The necessary `amplitude relationships between the exciting x and zcomponents for excitation of such a wave at the position of aperture48--49 is inherently obtained by the location of the aperture and therelative dimensions of slots 48 and 49 as defined above. Thus a portionof the wave energy in cavity 43 which is coupled into guide 40 willappear at terminal b only. The magnitude of this coupled energy isdetermined by the sizes and impedances of apertures 48-49 and 50-51. Itis easily Possible by well kno-wn techniques to match the impedance ofterminals a and b to that of cavity 43 by enlarging the apertures untilall wave energy at the frequency f1 applied at terminal a will appear atterminal b. This connection -is indicated schematically in Fig. 6 by thearrow 58 indicating progression at the frequency f1 in the sense from ato b.

A similar analysis of Wave energy applied at terminal d of guide 41 willshow that the components f2, which now induce clockwise rotatingcomponents in cavity 43, are coupled to terminal c of guide 40. Thecomponents f1 and the components fn which are not now resonant in thecavity 43 pass on to terminal a of guide 41. A similar coupling existsfor wave energy applied at terminals c and b of guide 40. Thus theresulting terminal connections are shown on Fig.- 6 by which wave energyat the frequency or in the band of frequencies f1 is coupled fromterminal a to b, from terminal b to c, from terminal c to d, and fromterminal d to a, successively. OnV the other hand, the components f2 arecoupled from terminal a to d, from terminal d to c, from terminal c tob, and from terminal b to a, successively. In addition, a reciprocalcoupling exists for the components fn between terminals a and d andbetween terminals c and b. This is a coupling characteristic similar tothat shown in Fig. 4 for the ernbodiment of the invention shown in Fig.3, but is obtained in Fig. 5 by a structure of substantially simplifiedconstruction.

In all cases it is understood that the above described arrangements areillustrative of a small number of the many possible specific embodimentswhich can represent applications of the principles ofthe invention.Numerous and varied other arrangements can readily be devised inaccordance with these principles by those skilled in the art withoutdeparting from the spirit and scope of the invention.

What is claimed is:

A two-branch directionally-selective microwave filter comprising asection of shielded transmission line adapted to support electromagneticwave energy of circular polarization, a polarization selectiveconnection at each end of said line for electromagnetic wave energy oflinear polarization, means for applying wave energy within a rst band offrequencies to said connection at one end and means for applying waveenergy within a second band of frequencies to said connection at theother end, a pair of degree differential phase shift elements disposedone in each end of said guide having the planes of phase shift thereofinclined at 45 degrees to said linear polarization, said planes of phaseshift being inclined to each other 9G degrees so that wave energy withinsaid rst band is converted into a circularly polarized wave rotating ina rst sense Within said guide as viewed in one direction along the axisof said guide and wave energy within said second band is converted intoa circularly polarized wave rotating in a sense opposite to said onesense as viewed in said one direction, a pair of conductive iriseslocated in a center portion of said line and spaced apart by aneffective guide wavelength that is longer than a multiple of one-halfwavelengths of said energy within said rst band and shorter than amultiple of one-half wavelengths of said energy within said second band,and means located between said irises for presenting a real permeabilityof one Value to wave energy Within said cavity rotating in a. rst sense`of circular polarization and a different value to waves Within saidcavity rotating in an opposite sense of circular polarization, saidmeans including an element of gyromagnetic material, and means formagnetizing said element to a point at which said elfective guidewavelength is substantially equal to a multiple of one-half of the guidewavelengths of energy within both said bands.

References Cited in the le of this patent UNITED STATES PATENTS Re.23,950 Bloch et al. Feb. 22, 1955 2,645,758 Van de Lindt July 14, 19532,702,351 Hershberger Feb. 15, 1955 2,720,625 Leete Oct. 11, 19552,755,447 Englemann July 17, 1956 2,887,664 Hogan c May 19, 1959 FOREIGNPATENTS 592,224 Great Britain Sept. 11, 1947 980,648 France Dec. 27,1950 OTHER REFERENCES Publication I, Van Trier, Experiments on theFaraday Rotation of Guided Waves, Applied Scientic Research, sect. B,vol. 3, pages 142-44.

Sakiotis et al., Microwave Antenna Ferrite Applications, Electronics,June 1952, pages 156, 158, 162 and 166.

Sakiotis et al., Proceedings of the IRE, January 1953, pages 87-93.

